{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### From Chapter 1 of Twomey (1977)\n",
    "\n",
    "$$ B(\\lambda, T) = \\alpha_{\\lambda} B(\\bar{\\lambda}, T) + \\beta_{\\lambda} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from bt2rad import bt2rad\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = np.arange(230,300,10)\n",
    "B = bt2rad(675., T)            # 675 cm-1 is near the center for the 15-um CO2 band"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1229d4c50>]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(T,B,'.')\n",
    "xlabel('Temperature (K)')\n",
    "ylabel('Radiance')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x122aba2e8>,\n",
       " <matplotlib.lines.Line2D at 0x122aba470>]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = np.polyfit(T,B,1)\n",
    "plot(T,B,'.', T,polyval(p,wn),'r--')\n",
    "xlabel('Temperature (K)')\n",
    "ylabel('Radiance')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x122ca69b0>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fhOvvdff3ge1m9hLQCDyTrfpEZBw7N8CqxdCfhFgclq6B6saoq5Ism+y7jyrd/TWAcFkRrv84sHPQfrvCdSISlc6WIBC8P1h2tkRdkUyCCYWCmVWa2R1m9mj4/jgzuzyDddgI63yUWq4wszYza9u9e3cGSxCRIWoWBD0EiwXLmgVRVySTYKI9hbuAx4Ajw/cvAl/bj+/XZWYzAcJld7h+F1A9aL8q4NWRTuDuP3b3BndvmDFjxn6UICITUt0YDBl95noNHRWRiYbCEe5+P5ACcPc+oH8/vt8aYGn4einwyKD1F5lZmZnNAY4GdGVLJGrVjbDgOgVCEZnohea3zayccEjHzJqAP411gJndQ3BR+Qgz2wX8LXAzcH849PQycD6Auz9vZvcDvwf6gK+6+/6EjoiIHICJhsJfEfw1P9fM/h2YAZw31gHufvEom84cZf+bgJsmWI+ITIJEd4K2rjYaKhuoq6iLuhyZBBMKBXffZGZnAPMILgpvdfferFYmIpFKdCdYvm45yf4k8Vic5kXNCoYiMNG7j74KfMTdn3f3LcBHzOyq7JYmIlFq62oj2Z8kRYreVC9tXW1RlySTYKIXmpe7+5sDb9x9D7A8OyWJSC5oqGwgHosTsxhTSqbQUNkQdUkyCSZ6TaHEzMzdBy40x4B49soSkajVVdTRvKhZ1xSKzERD4TGCu4ZWENyBdCWwNmtViUhOqKuoUxgUmYmGwt8A/wP4CsGF5nXAymwVJSIi0Zjo3Ucp4F/CLxERKVATCgUz+0/ADcDs8BgD3N1rs1eaiIhMtokOH90BfB1oZ/+mtxARkTww0VD4k7s/mtVKREQkchMNhSfN7HvAQ8D7AyvdfVNWqhIRkUhMNBQ+FS4Hf3rFgc9kthwREYnSRO8++nS2CxERkehN+BnNZvafgeOBqQPr3P3vslGUiIhEY6IT4q0ALgSuIbgd9XyC21NFRKSATHRCvNPc/UvAHne/ETiVoY/PFBGRAjDRUHg3XL5jZkcCvcCc7JQkIiJRmeg1hV+a2UeB7wGbCO480txHIqNo37GH1o4emmrLqZ89PepyRCZsoncffSd8+aCZ/RKY6u5jPqNZpFi179jDkpWtJPtSxEtLWL2sScEgeWPMUDCzz7j7r83siyNsw90fyl5pIvmptaOHZF+KlENvX4rWjh6FguSN8XoKZwC/Bs4eYZsTfMJZRAZpqi0nXlpCb1+KKaUlNNWWR12SyIRZ+DC1vNTQ0OBtbXpurOQeXVOQXGZm7e4+4vNVxxs++quxtrv7rQdSmEihqp89XWEgeWm84aNDwuU84BRgTfj+bODpbBUlIiLRGDMUwg+qYWbrgJPdfW/4/gbg51mvTiRf7dwAnS1QswCqG6OuRmTCJvo5hVlActD7JFCT8WpECsHODbBqMfQnIRaHpWsUDJI3JhoKdwMbzOwXBHcdnQv8NGtVieSzzpYgELw/WHa2KBQkb0z0w2s3mdla4M/CVZe6++bslSWSx2oWBD2EgZ5CzYKoKxKZsAlPne3u7Wa2k3DqbDOb5e4vZ60ykXxV3RgMGemaguShCYWCmS0GbgGOBLoJrjH8B8HzFURkuOpGhYHkpYnOkvodoAl40d3nAJ8F/j1rVYmISCQmGgq97t4DlJhZibs/CdRlsS6RvJboTrDyuZUkuhNRlyLyoUz0msKbZvYRgg+srTazbqAve2WJ5K9Ed4Ll65aT7E8Sj8VpXtRMXYX+hpL8MNGewjnAO8DXgbXAHxh5kjyRotfW1UayP0mKFL2pXtq6ND+X5I+J3pL6dvgyBawysxhwEbA6W4WJ5KuGygbisTi9qV6mlEyhoXLEecdEctJ4E+IdCnwV+DjBvEePh++/ASRQKIh8QF1FHc2LmmnraqOhskFDR5JXxusp3A3sAZ4BlhGEQRw4x911BU1kFHUVdQoDyUvjhUKtu38SwMxWAq8DswYmxhMRkcIy3oXm3oEX7t4PbM9EIJjZ183seTPbYmb3mNlUMzvczB43s23hUpPRi4hMsvFC4SQzeyv82gucOPDazN7an29oZh8H/hJocPcTgIGL1t8E1rv70cD68L2IiEyiMUPB3WPufmj4dYi7lw56fegBfN9SYJqZlQIHAa8S3Pa6Kty+CvjCAZxfRET2w0Q/p5Ax7v4K8I/Ay8BrwJ/cfR1Q6e6vhfu8BlRMdm0iIsVu0kMhvFZwDjCHYIK9g83sv32I468wszYza9u9e3e2yhQRKUqTHgoEk+ltd/fd7t4LPAScBnSZ2UyAcNk90sHu/mN3b3D3hhkzZkxa0SIixSCKUHgZaDKzg8zMgDOBFwg+HLc03Gcp8EgEtYmIFLUJP2QnU9z9t2b2ALCJYFK9zcCPgY8A95vZ5QTBcf5k1yYiUuwmPRQA3P1vgb8dtvp9gl6DiIhEJIrhI5ERte/Yw+1PvkT7jj1RlyJStCLpKYgM175jD0tWtpLsSxEvLWH1sibqZ+tD7SKTTT0FyQmtHT0k+1KkHHr7UrR29ERdkkhRUihITmiqLSdeWkLMYEppCU215VGXJFKUNHwkOaF+9nRWL2uitaOHptpyDR2JREShIDmjfvZ0hYFIxDR8JCIiaQoFyR07N0DLLcFSRCKh4SPJDTs3wKrF0J+EWByWroHqxqirEik66ilIbuhsCQLB+4NlZ0vUFYkUJYWC5IaaBUEPwWLBsmZB1BWJFCUNH0luqG4Mhow6W4JA0NCRSCQUCpI7qhsVBiIR0/CRiIikKRQkZyS6E6x8biWJ7kTUpYgULQ0fSU5IdCdYvm45yf4k8Vic5kXN1FXURV2WSNFRT0FyQltXG8n+JClS9KZ6aetqi7okkaKkUJCc0FDZQDwWJ2YxppRMoaGyIeqSRIqSho8kJ9RV1NG8qJm2rjYaKhs0dCQSEYWC5Iy6ijqFgUjENHwkIiJpCgUREUlTKIiISJpCQURE0hQKIiKSplAQEZE0hYKIiKQpFPJc+4493P7kS7Tv2BN1KSJSAPThtTzWvmMPS1a2kuxLES8tYfWyJupnT4+6LBHJY+op5LHWjh6SfSlSDr19KVo7eqIuSUTynEIhjzXVlhMvLSFmMKW0hKba8qhLEpE8p+GjPFY/ezqrlzXR2tFDU225ho5E5IApFPJc/ezpCgMRyRgNH4mISJpCId/t3AAttwRLEZEDpOGjfLZzA6xaDP1JiMVh6Rqoboy6KhHJY+op5LPOliAQvD9YdrZEXZGI5DmFQj6rWRD0ECwWLGsWRF2RiOS5SIaPzOyjwErgBMCBy4CtwH1ADdAJXODumrthLNWNwZBRZ0sQCBo6EpEDFFVP4QfAWnc/BjgJeAH4JrDe3Y8G1ofvZTzVjbDgOgWCiGTEpIeCmR0KnA7cAeDuSXd/EzgHWBXutgr4wmTXJiJS7KLoKdQCu4GfmNlmM1tpZgcDle7+GkC4rIigtryT6E6w8rmVJLoTUZciIgUgimsKpcDJwDXu/lsz+wEfYqjIzK4ArgCYNWtWdirME4nuBMvXLSfZnyQei9O8qJm6irqoyxKRPBZFT2EXsMvdfxu+f4AgJLrMbCZAuOwe6WB3/7G7N7h7w4wZMyal4FzV1tVGsj9JihS9qV7autqiLklE8tykh4K7/xHYaWbzwlVnAr8H1gBLw3VLgUcmu7Z801DZQDwWJ2YxppRMoaGyIeqSRCTPRfWJ5muA1WYWBzqASwkC6n4zuxx4GTg/otryRl1FHc2LmmnraqOhskFDRyJywCIJBXdPACP9WXvmZNeS7+oq6hQGIpIx+kSziIikKRRERCRNoSAiImkKBRERSVMoiIhIWtGGQvuOPdz+5Eu079BErCIiA4ryyWvtO/awZGUryb4U8dISVi9ron729KjLEhGJXFH2FFo7ekj2pUg59PalaO3oibokEZGcUJSh0FRbTry0hJjBlNISmmrLoy5JRCQnFOXwUf3s6axe1kRrRw9NteUaOhIRCRVlKEAQDAoDEZGhinL4SERERla8obBzA7TcEixFRAQo1uGjnRtg1WLoT0IsDkvX6MH3IiIUa0+hsyUIBO8Plp0tUVckIpITijMUahYEPQSLBcuaBVFXJCKSE4pz+Ki6MRgy6mwJAkFDRyIiQLGGAgRBoDAQERmiOIePgER3gpXPrSTRnYi6FBGRnFGUPYVEd4Ll65aT7E8Sj8VpXtSs5xyLiFCkPYW2rjaS/UlSpOhN9dLW1RZ1SSIiOaEoQ6GhsoF4LE7MYkwpmUJDZUPUJYmI5ISiHD6qq6ijeVEzbV1tNFQ2aOhIRCRUlKEAQTAoDEREhirK4SMRERmZQkFERNIUCiIikqZQEBGRNIWCiIikKRRERCTN3D3qGvabme0GdhzAKY4AXs9QOVEqlHaA2pKLCqUdoLYMmO3uM0bakNehcKDMrM3d8/7jzIXSDlBbclGhtAPUlonQ8JGIiKQpFEREJK3YQ+HHUReQIYXSDlBbclGhtAPUlnEV9TUFEREZqth7CiIiMohCQURE0go2FMys2syeNLMXzOx5M7s2XP8dM3vWzBJmts7Mjhx0zLfM7CUz22pmn4uu+n1Ga8eg7X9tZm5mRwxal3PtgDF/JzeY2Svh7yRhZn8x6Ji8aku47Zqw3ufN7P8MWp9XbTGz+wb9TjrNLDHomJxryxjtqDOz1rAdbWbWOOiYnGsHjNmWk8zsGTN7zsz+1cwOHXRMZtri7gX5BcwETg5fHwK8CBwHHDpon78EVoSvjwN+B5QBc4A/ALFcbUf4vhp4jOADfEfkcjvG+Z3cAPz1CPvnY1s+DTwBlIXbKvK1LcP2uQX4di63ZYzfyTrg8+H6vwCeyuV2jNOWjcAZ4frLgO9kui0F21Nw99fcfVP4ei/wAvBxd39r0G4HAwNX2s8B7nX39919O/AS0EjERmtHuPmfgP/JvjZAjrYDxm3LSPKxLV8Bbnb398Nt3eEh+dgWAMzMgAuAe8JVOdmWMdrhwMBf1IcBr4avc7IdMGZb5gFPh7s9DvzX8HXG2lKwoTCYmdUA84Hfhu9vMrOdwBLg2+FuHwd2DjpsF2P/gzXpBrfDzBYDr7j774btlvPtgA/+ToCrw2G9O81serguH9vyCWCBmf3WzH5jZqeEu+VjWwYsALrcfVv4PufbMqwdXwO+F/4//4/At8Ldcr4d8IG2bAEWh5vOJxgtgAy2peBDwcw+AjwIfG2gl+Du17t7NbAauHpg1xEOz5n7dQe3A+gDrmdfoA3ZdYR1OdMOGPF38i/AXKAOeI1gqALysy2lwHSgCfgGcH/4l3Y+tmXAxezrJUCOt2WEdnwF+Hr4//zXgTsGdh3h8JxpB4zYlsuAr5pZO8GwUnJg1xEO36+2FHQomNkUgh/oand/aIRdfsa+7tcu9qUuQBX7upmRGqEdcwnGDX9nZp0EtW4ys4+Rw+2AkX8n7t7l7v3ungKa2dftzbu2ENT8kAc2ACmCicvysS2YWSnwReC+QbvnbFtGacdSYOD1z8nj/77c/T/cfZG71xME9R/C3TPXlqgvqGTriyA5fwp8f9j6owe9vgZ4IHx9PEMv1HSQAxedRmvHsH062XehOSfbMc7vZOag118nGBvN17ZcCfxd+PoTBF16y8e2hNvOAn4zbF1OtmWM38kLwJ+Hr88E2nO5HeO0ZeDGhZJw+2WZbkvkjc/iD/XPCLpPzwKJ8OsvCJJ3S7j+XwkuPg8ccz1B8m4lvFsh6q/R2jFsn3Qo5Go7xvmd3A08F65fMywk8q0tceD/hv+NbQI+k69tCbfdBVw5wjE515Yxfid/BrSH/2j+FqjP5XaM05ZrCe5EehG4mXBWiky2RdNciIhIWkFfUxARkQ9HoSAiImkKBRERSVMoiIhImkJBRETSFAqSl8ysfNAMnn8cNstqPOr6RmJml4UfMMzW+Q82s6fMrMTMjho2q+mVZrbRzA4zs++b2enZqkPyW2nUBYjsD3fvIZgWAzO7Afh/7v6PkRYV1BJz9/5RNl9G8NmFP36I85W6e98Ed18G/NzdU8HMGulzXErwobrPuPufzOw24Ifsm1hNJE09BSk4ZrbUzDaEvYZ/Dv9yLjWzN83se2a2ycweM7NPhZPWdVj4DAczW2Zmvwi3bzWz/zXB8/69mW0AGs3sxvCv8i1mtnZu6REAAALFSURBVMICFxKE2MAzCuJmtsvMPhqeu8nMnghf/72Z/cjMHgd+En6PW8Pv/ayZLRul6UuAR4b9LC4BrgMWufsbAO7+B2Cmmc3I6A9eCoJCQQqKmZ0AnAuc5u51BL3hi8LNhwHr3P1kgonEbiCY9uB84O8GnaYxPOZk4BILHtIy3nk3uXujuz8D/MDdTwE+GW47y93vI/hU6oXuXufuScY2Hzjb3f87cAXQ7e6NwCkEE6LNGtbuqUCVu+8atLoWuJUgELoZajNw2jg1SBHS8JEUms8S/MPZFg6hTGPflMLvuvvj4evngD+5e5+ZPQfUDDrHY+6+B8DMHiaYcqB0jPMmgV8MOv5MM/sGMJVgMrx24NEP2Y5H3P298PUi4FgzGxxCRwMvD9q/Anhj2Dm6gL0Ekz7eNmxbN3AkIsMoFKTQGHCnu//vISuD2T4H/3WeAt4f9Hrw/wvD537xcc77rofzxZjZQQTj9Se7+ytm9vcE4TCSPvb11ofv8/awNl3l7utHOQ/Au6Oc4/PAv5lZd9hbGTA1PEZkCA0fSaF5ArjAwmdWh3cpzRrnmOEWmdlHw3/gzwH+/UOcdxpByLxuZoewb2p2CP5qP2TQ+06gPnw9eL/hHgOuCgMIM5tnZtMG7+Duu4Gpw++8cvcugplOv2dmnx206RMEk/aJDKGeghQUd3/OzG4EnjCzEqCX4M6bDzO3/L8RPGtjLnC3uycAJnJed+8xs1UE/+DuYOgTzH4CrDSzdwmuW9wANJvZH4ENY9TzI2AWkAiHrroJwmq49QTXCZ4aVtMfzOwLwL+a2TkEQ2c1BNcVRIbQLKkig4R39pzg7l+LupYPy4JHf17l7peOs9/5wHHufuPkVCb5RMNHIgXC3TcSXD8Y7/9rA/5pEkqSPKSegoiIpKmnICIiaQoFERFJUyiIiEiaQkFERNIUCiIikvb/AWyrvpyapaD0AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure()\n",
    "plot(T, bt2rad(675., T), '.', T, bt2rad(700., T), '.', T, bt2rad(725., T), '.')\n",
    "xlabel('Temperature (K)')\n",
    "ylabel('Radiance')\n",
    "legend(('675 cm-1', '700 cm-1', '725 cm-1'), loc='best')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "p1 = np.polyfit(T, bt2rad(675., T), 1)\n",
    "p2 = np.polyfit(T, bt2rad(700., T), 1)\n",
    "p3 = np.polyfit(T, bt2rad(725., T), 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([   1.31488375, -250.3667531 ]),\n",
       " array([   1.31639086, -253.49107034]),\n",
       " array([   1.3123575 , -255.37736595])]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[p1, p2, p3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[212.26116891,   0.        ,   0.        ],\n",
       "       [  0.        , 212.87461617,   0.        ],\n",
       "       [  0.        ,   0.        , 213.48193671]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = 200.\n",
    "a = np.array([p1[0], p2[0], p3[0]])\n",
    "b = np.array([p1[1], p2[1], p3[1]])\n",
    "\n",
    "B = bt2rad(np.array([675., 700., 725.]), T)\n",
    "\n",
    "np.linalg.inv(a*np.identity(3)) * (B - b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
